Variable magnification optical systems



H. H. HQPKINS VARIABLE MAGNIFICATION OPTICAL SYSTEMS 3 sheets-sheet iFiled Oct. 27, 1953 amr-.......l'n

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VARIABLE Filed. Oct. 27, 1955 H. H, HQFKNS IJAGNIFICATION OPTICALSYSTEMS 3 Sheets-Sheet 3 United States Patent O VARIABLE MAGNIFICATIONUPTiCAL SYSTEMS Harold Horace Hopkins, London, England, assignor` .to W.Watson @a Sons Limited, London, England, a British company Applicationetober 27, 1953, Seriai No. 383,499

Claims priority, appiieaton freat Britain Gctober 5, 1951 7 Cairns. (ci.sti- 57) This application is a continuation-in-part of my applicationSerial No. 313,205, filed October 6, 1952, now abandoned.

The invention relates to variable magnification optical systems and ismore particularly concerned with optical systems of the kind(hereinafter referred to as the kind described) for producing an imageof continuously variable size of an object at a fixed distance from thesystem and comprising two normally stationary lenses, having powers oflike sign (i. e., both positive or both negative),

and two axially movable lenses, having powers of like sign f which isopposite to the sign of the powers of the normally stationary lenses,all of which lenses are arranged on a common optical axis with themovable lenses between and spaced from the two normally stationarylenses, and in combination with the lenses magnification 'varying meansfor continuously and simultaneously differentially moving the movablelenses in the axial direction of the system according to a law such thatthe distance from the normally stationary lenses at which the image ofan object at a fixed distance from the normally stationary lenses isaccurately focussed remains constant, while the size of the said imageis continuously varied during the operation of the magnification varyingmeans, in which system the movable lenses and their range of movementare such that, for one final image position of the system, at oneposition (hereinafter referred to as their mean position) of theirmovement they have a joint magnification of minus l.

The movable lenses are movable in one axial direction away from theirmean position to a far position, spaced from their mean position, andare preferably also movable in the opposite axial direction from theirmean position to another far position, spaced from their mean position.rille, or each, far position may advantageously be a limit of the rangeof movement of the movable lenses.

The two movable lenses are preferably movable between two far positionssuch that their joint magnification when they are at one of the farpositions is equal to the reciprocal of their joint magnification whenthey are at the other far position, for at least one final imageposition of the system.

The term normally stationary lens is to be understood to mean a lenswhich remains stationary during the continuous variation of the size ofan image of an object at a fixed distance from the system.

Examples of optical systems of the kind described are described andclaimed in the specifications of United States Patents Nos. 2,501,219,2,514,239, 2,537,561 and 2,566,889, and pending application Serial No.236,482, now Patent No. 2,663,223, dated December 22, 1953.

The invention is more especially but not exclusively, concerned withsystems of the kind described in which the normally stationary lensesare positive and the movable lenses are negative (i. e. as described inUnited States patent specification No. 2,514,239).

In systems of the kind to which the invention relates, one or both ofthe two normally stationary lenses may be FPice mounted for adjustingmovement along the optical axis and focus-adjustment means may beprovided and may be operable, independently of the magnification-varyingmeans, to move the or each adjustably mounted stationary lens to effectfocussing of the system, as described and claimed in United Statespatent specification No. 2,566,889 and in British patent specificationNo. 639,611. It will be appreciated that although the operation of thefocus-adjustment means is described in that specification with specialrelation to initial focussing of the system on to a fixed object beforeoperation of the magnification-varying means, the focus-adjustment meansspecifically described in that specification may equally well beadjusted during operation of the magnification-varying means withoutalteration to the structure specifically described in thatspecification. Thus the magnification of the system described in thatspecification may also be varied while the focussing of the system isadjusted independently to keep in focus an object which moves during thevariation of magnification.

Further, in such system each of the four lenses may be a compound lenscomprising two or more component lenses in contact or spaced apart by afixed distance or fixed distances, one or more of which component lensesmay comprise two or more lens elements in contact.

lt is an object of the present invention to provide an improved opticalsystem of' the kind described, in which the aberrations are reduced orsubstantially corrected.

The primary aberrations which may occur in systems of the kind describedare of seven main types usually denoted by symbols, viz: Si=spliericaiaberrations, S2: coma, Sszastigmatism, S4=field curvature, S5=distortion, L--axial chromatic aberration, and Tzchromatic variation ofmagnification.

lt is well known that when the chromatic aberrations L and T of a lenssystem are corrected for one position of the object and stop, they willalso be corrected in all positions of the object and stop. Consequentlythe system may be substantially corrected for chromatic aberrations byemploying achromatic lenses throughout the system. It then follows thatthe system will have substantially no chromatic aberrations no matterhow the relative positions of the movable lenses vary during thevariation of the image size.

Further it is well known that the eld curvature Si of a lens system isdetermined by the construction of the individual lenses and is quiteindependent of the positions of the object and the stop. Consequentlythe system may be made substantially free of field curvature for allpositions of the movable lenses by so arranging the construction of thesystem that it is free from field curvature for any one position of themovable lenses.

The invention provides in one of its aspects a variable magnificationoptical system of the kind described, in which the lenses are such thatthe respective differences between the values of spherical aberration,coma, astigmatism and distortion produced by the movable lenses whenthey are at their mean position and the corresponding values of thosefour aberrations produced by the movable lenses when they are in theirfar position or in one or each of their far positions, are substantiallyequal and opposite to the respective differences between the values ofspherical aberration, coma, astigmatism and distortion produced by thesaid two normally stationary lenses when the movable lenses are at theirmean position and the corresponding values of those four aberrationsproduced by the said two normally stationary lenses when the movablelenses are at the said far position, whereby each of the said fouraberrations has substantially the same magnitude and sign when themovable lenses are in their far position or one J or I"each of'their-'far 'positions "'as when they are in their mean position.

The lenses are preferably'such that the coma and distortion produced bythe movable lenses are zero when the Vmovable lenses are "at vtl-iieir"mean position 'and Athe coma and distortion produced by the said twonormally stationary lenses are Zerowhen tlie iiiov'able 2lenses Avare in'their meanpositio'n, whereby the coma-and distortion of the system 'arezero when the movable llenses itare in1 their mean position'a'nd alsowhen themov'able lenses areat ytheir far -position or at either of theirfar positions.

y The movable ylenses preferably are compound and optically identical,-except, it'ma'ybe, in respect -of "their apertures,`- and larearranged'with their refr'acting surfaces symmetrically positioned aboutyapoint on the 'axis -mdway betweenthe movable lenses.

Thesaid two normally "stationary lenses preferably-arecompoundand'optically identical, '^ex`cept,'it'may be, inrespect'of'their apertnres'and va'rearranged with their refractingsurfaces symmetrically lpositioned about a point on 'the axis mid-wayvbetween the 'said two= normally stationary lenses.

Forthe consideration ofthe theory ofthe system it is convenient toassume that the effective stop' of the system is'positioned betweenthetwo movable lenses and is preferably such as the ratio of theincidence height of theprincipal ray to the incidence height of theparaxial ray is substantially as much negative as one of the movablelenses as it is positive at theother movable lens. Nevertheless, inpractice the eifective stopmay be situated in any one of a number ofpositions, since if the aberrations of the system are corrected for anyone posiltionfof the effective stopthey are automatically corrected forlall other positions of the eliective stop, at least so far as primaryaberrations are concerned. As a practical example the stop may be in theform of an apertured Adiaphragm and may be positioned at a fixed axialdistance from, and be arranged for movement with, that `oneof the twomovable lenses which is nearer'to the vfinal, image position of thesystem,lthe arrangement being, for example, as described in pendingapplication Serial No.' 236,482, now Patent No. 2,663,223.

It can `beshowny from optical theory that when the hereinbeforementioned preferred arrangements are' employed, the values of thespherical aberrationSi,l astigmatisniSs and field Acurvature S4 of themovable lenses atione of their far'porsitions are respectivelysubstantially equal in magnitudeia'nd sign to the corresponding values of those three aberrations of the movable lenses when they are' at theirAother lfar position.v n l 'It'vcan also be shown 'from voptical'theory` that when the 'hereinbefore mentioned preferred arrangements areemployedfthe values ofthe (joint) coma S2, and distortion S5 of vthemovable lenses at one of their far posijtions' are respectivelyvsubstantially equal in magnitude and 'opposite 'in sign'to theco/rresponding'values of those two aberrations of the movableilenses'when`they are at their other far position.

Further, the respective diiferences'between the values of the sphericalaberration' Si, comaSzfastigm'atism S3, field curvature S4' anddistortion S5 of 'the movable lenses at one of their far positions, andthe corresponding values of those tive aberrations of the movable'lenses when 'they are at their mean position are functions'fonly of thefollowing, namely the spherical aberration and the central coma of eachof the movable lenses when they are'at their mean position. Theconstants that appear in the expressions for those differences involveonly the P etzval sum for the movable lenses, theV power of each Aof themovable lenses, and the effective positions of the object,

image and stop.

The term central coma of a lens is to be understood to mean the coma ofthe lens if the Yeife'ctive stop is assumed to be placed in contact withthe lens. l By`the Petz'val sum for the movable lenses is meansv the sum4 of the powers of the separate lens elements divided by the respectiverefractive -indices of the glasses of which they are made.

For convenience the values respectively of the spherical aberration andcentral coma of that one of the two movable lenses which is nearer tothe object, when the movable lenses are in their mean position, will behereinafter denotedby (S1)z and (S2)2 respectively.

It can also be shown from optical theory that analogous resnltsareobtained 'for the joint aberrations'of the two normally stationarylenses when the movable lenses are in their mean and far positions.Thus, if (S1)1 and (S2)1 denote respectively ythe spherical aberrationand central coma` of that one of the two normally stationary lenseswhich is nearer to the object, when the movable lenses are in their meanposition, there may be expressed in terms of (S1)1 and (S2)1 therespective differences between thevvalues of spherical aberration Si,coma S2, 'astigmatism-Ssanddistortion Ss'produced jointly by the t'wonormally stationary lenses when the two rmovable lenses are at either oftheir far positions, andthefcorresp'on'ding valuesofithose-fouraberrations when theftwo m'ovablelenses areat ltheir ymean position. TheVjoint iield curvature ofthe normally stationary lenses does not varyasE the 'movable' lenses are4 moved, and further, there isno-theoretical riee'dto :assume that the normally stationary lensesarethi-n, =as the effective object and image positins'for thoselenses doVnot change as the movable lenses-are moved.

The"value 'of (Si)1, (32h, (S02 and (S2)2 which it is necessary 'tolemployi-inV order-"to-produce a system in accordance withithee-invention' may thus be determined by solving theY following foursimultaneous equations:

"d(-S`1)m-}-'d(}S'i)ns-`i0 'MS2 )"n'id('Sz)ns=v0 'd(S3)m-|d(S)'ns=0=d(S5)m-id(S5)ns=0 where: e

-The'operator "d*denotes thedilierence between the value of anaberration produced when the movable lenses are at either of their farVpositions and the corresponding valuev of that aberration ,when themovable-lenses are l at their mean position. Y The subscript mdenotes-an aberration producedjointly by thefmovable lenses, and Thesubscript ns denotes anaberration' produced jointly by the twonormallystationary lenses.

Any'compound lens -consistingof two' or more lenses in contact,l in `anyof" the above described symmetrical arrangementa'may be replacedbyanother compound lens consisting of two or more lenses-in `Contact and'destroying the symmetry, providing that thel power, the sphericalaberration, central comaand Petzval sum-of the replacing and replacedcompound lenses are substantially the same at' anyone-positioniin-therange of'movement of the movablejlenses. AThis follows from 'the fact,which may be provedltheoretically, that'thefspherical aberration,central comaand Petzval sum ofa sys'temof thin'lensesincontact-determine uniquely all-the aberrations of that :system of thinlenses, irrespective ofthe position of the-eiective positions of theobject'and stop-for that system. IThus considerations of symmetrysimplify the theory of the 'systems according to the invention, but inpractice departures from symmetry may be advantageous` and suchdepartures are within the scope of the invention. For eX- ample, it issometimes possible to replace a lens in which at some surface the anglesof incidence of one or more rays are large by a lens in which theseangles are less, with a consequent reduction in higher order aberration.Symmetrical arrangements however employ identical lenses in differentpositions in the system and consequently are preferred on economicgrounds.

One or more additional normally stationary lens may be added, e. g.between the rear one of the said two ncrmally stationary lenses and theimage receiving position, to cancel out all or some of the remainingaberrations of the system when the movable lenses are at their meanposition. The additional normally stationary lens or lenses will thenalso substantially cancel out the remaining aberrations of the systemwhen the movable lenses are at either of their far positions and also toa very large extent when the movable lenses are at any other position intheir range of movement, provided that the aberrations of the additionalnormally stationary lens are small enough for displacement of theeective stop position for that lens to produce only negligible changesin those aberrations. The additional normally stationary lens or lensesmay conveniently convert the system from an afocal one to one of nitefocal length.

Each movable lens may comprise two doublet component lenses spaced apartby a fixed axial distance. The spherical aberration and central coma ofone doublet in cach movable lens, when the movable lenses are at theirmean position, may be chosen independently of the correspondingconstants cf the other doublet in each movable lens. Consequently twoadditional independent design variables are available and may be chosenso as to satisfy the following twcadditional conditions, namely that thejoint spherical aberration of the four lenses (two movable and twonormally stationary) shall be zero and that the joint astigmatism of thefour lenses shall have a desired value. For example the value of thatastigmatism may be chosen in relation to the total eld curvature of thefour lenses so that the tangential image surface lies in the paraxialfocal plane. The system is in that case substantally completely conectedfor primary aberrations.

The foregoing theoretical considerations apply to a four lens systemwhich is afocal or which is such that the object and image aresymmetrically positioned with respect to the system.

in a modification of the hereinbefore mentioned aspect of the inventionthe lenses may be such that instead of fulfilling the condition that thedifference between the value of distortion produced by the movablelenses when they are at their mean position and the value of thedistortion produced by the movable lenses when they are at their farposition, or one of their far positions, is substantially equal andopposite to the difference between the value of distortion produced bythe two non mally stationary lenses when the movable lenses are at theirmean position and the value of the distortion produced by the twonormally stationary lenses when the movable lenses are at the said farposition.

Such a modified system has Zero spherical aberration, zero com andsubstantially constant astigmatism over the range of movement of themovable lenses. This system may be employed with an additional normallystationary aplanatic lens having a value of astigmatism which cancelsout that of the system. Such cancellation is preferably arranged to beexact for both far positions and the mean position of the movablelenses. In that arrangement the cancellation is very nearly exact forall other positions of the movable lenses, as only the effective stopposition for the additional normally stationary lens changes on movementof the movable lenses and, since the additional stationary lens isaplanatic, the astigmatism of that lens will remain constant and of avalue which is equal and opposite to that of the rest of the system,during the movement of the movable lenses. Distortion remains, but inmany applications quite large distortion can be tolerated.

A specific construction of an optical system according to the inventionwill now be described by way of example and with reference to theaccompanying drawings, in which:

Figure l is a diagrammatic longitudinal section through the systemshowing the arrangement of the lenses,

Figure 2 is a side view of the system with part of the cover removed andwith part of the focussing control system omitted for the sake ofclarity,

Figure 3 is a plan View of the system with part of the cover removed,

Figure 4 is a front View 0f the system,

Figure 5 is a detail View showing the underside of the carrier, and

Figure 6 is a detail View showing the focussing control arrangement.

The system, in this example, comprises two normally stationary positivecompound achromatic lenses 21, 24 and two movable negative compoundachromatic lenses 22, 23. The lens 21 comprises three component lenses1l, l2, 13 having optical surfaces ri, r2, ra, r4, rs. The components12, 13 are in contact. The components l1, 12 are spaced apart by a fixeddistance. The lens 2d comprises three component lenses 1S, 19, 2t)haring optical surfaces :'12, 1'13, rit, rte, rie. The components i3, 19are in contact. The components i9, 2l) are spaced apart by a fixeddistance.

The lens 22 comprises two component lenses ld, l5 in contact and havingoptical surfaces rs, rr, rs. The lens 23 comprises two component lenses16, 17 in contact and having optical surfaces r9, rio, r11.

The various component lenses are made of glasses having the followingproperties, and the component lenses or elements have the followingaxial thicknesses (in inches):

A :tial Thick- Nd is the refractive index for the d-line. V is thereciprocal of the dispersive power.

The air spaces between the elements 1l and l2, and 19 and 20,respectively are (in inches):

The optical surfaces have the following radii (in inches):

The radii are expressed as minus quantities in the case of surfaceswhich are concave towards light entering the system through the lens 21,which in normal use is the front lens.

7 w (y The lenses have the following diameter (in inches): f

Lens: Diameter '21 4.6 '122 '28 23 2 3 24 4 6 S1 Sz 5; Magnification 0.74361 2. 62303 6.77110 1/224 Far position.

1. 44660 2. 04676 6. 64330 1/2 3.36855 0. 76702 6.00127 1/1/'2' 4. 91076`0. 31622 4. 91076 -1 Mean posmon. 6. 00127 0. 76792 3. 36655 J2 6.643302. 04875 1.44669 -2 n 6. 77110 2. 62303 0. 74361 2. 24 F111y posttmn.

`An aperture stop 25 is-positioned'between the. lenses 23 and 24 at anaxial distance of` 2.5'from the axial midpoint between the `lenses 22and23. yThe maximum diameter of-thelight beam transmitted along the axis ofthe system is 3.2 at surface r16.

The two lenses'21an'd 24 are carried in cells 51, 52

mounted in end plates 53, '54 at the ends of the top face of arectangular'base plate 55 which extends horizontally forward from thefront of the camera. 'Two straight rods or tubes'56 extendalong the topface of the base plate`55 along the length vthereof from one end platetothe other,

parallel to the-sidesof the base plate. A carrier 57, com y prising asmaller rectangular plate 59, has longitudinal grooves 58 in one of itsfaces and those grooves 58 rest over the rods 56 so rthat the carrier 57is slidable along them. The carrier 57 has above and spaced from itsupper face two rods or tubes61 extending longitudinally from one end ofthe carrier 57 to the other near and parallel to the sides of thecarrier, the rods 61 being secured to brackets 62 on the carrier. Thelenses 22 and 23 are mounted incells 63, 64 attached to sleeves 65 whichslide along the rods 61. The two sleeves 65 are connected in pairs bymembers 66 which each carry a small roller -167 rotatableaboutvavertical axis. The two rollers 67 contact diametrically oppositeparts of the periphery of a cam 68 which is carried on a short verticalshaft extending through the carrier plate'59 and carrying, at the lowerface of the carrier plate, a gear wheel'71fwhich -is'fin engagementwitha worml 72.

The lower face ofrthe carrier has securely attached `to it a nut 73 inengagement with a` lead screw 74 which is journalled in brackets 75-securedto the base plate 55 and may be rotated so as to move thecarrier 57 along the base-plate 55. YThe lead-screw 74 is connectedthrough an extension shaft 77, gears 76 and an idler gearw82'1to a shaft73 running lparallel to the lead-screw and also journalled in the"brackets '75. The Worm 72 isslidable along the shaft 78 and has a keyengaged with .a key way 81 in the shaft'78 for rotation with that shaft.The Worm 72 lies between two brackets 83 extending downward from thevcarrier so that the worm is constrained to move with the. carrier andthereby to remain .in engagement with the gear` 71 on the cam shaft.Consequently on rotation of the 'lead-screw 74 the cam 68 rotates whilethe carrier is'fmoved. yTheI two sleeves :on each Aof the tubes ontheca11ier\.-are,spring-urged'towards one another,

`8 in. engagement with the cam 68. The cam .63 is of symmetriclelongated.shape and is arranged so that, "in accordance with the opticalrequirements, the lenses '22, 23 approach oneanother to a minimumseparation and then move apart again to a maximum separation while theyare bothmoved along the base-plate from one extreme position to theother. Back-lash in the gearing is reduced to a minimum by accuratemachining and if desired the'idler wheel 82 may be urged into evencloser engagement with the gears'7'6 by means of a strong spring.

The lead-screw .shaft 77 carries a chain wheel 9.1 connected by adriving chain 92 to a chain wheel'93 on a shaft 94 which isjournalled-in brackets 95 on the 'base plate 55. The shaft 94 is movableaxially in the brackets '95 and has a'key-way 96 into which the chainwheel 93 is keyed, e.g. by grub-screws'98, for rotation with the shaft94,'being held against axial movement by the adjacent bracket 95 and asleeve'97. The shaft 94 isprovided with a control handle 101 by means ofwhich it may be rotated or moved axially.

The cell 51 carrying the lens 21 is attached to aslide member 102 whichis slidable along rods or tubes 103, extending between the end plates'53, 54, to move the lens 21 axially for focussing the system on to anyparticular object at a distance from innity to about 13 feet 9 inchesaway from the system. The range of movement of the cell 51 isfrom theposition shown in full lines to that shown in chain lines in Figure 2.The slide member .102

is connected by a pivoted link to an arm 104 rigidlyV attached to oneend of a shaft 105 journalled in blocks rigidly mounted on the rods 103.The other end of the shaft 105 (see Figures 3 and 6) is rigidly securedto an arm 106 having a slot 107 sliding on a headed stud 108 provided ona sleeve 109 rigidly secured to the shaft 94. Axial movementfof theshaft 94 as aforesaid, consequently produces corresponding axialfocussing movement of the lens cell 51.

An iris diaphragm 111, constituting the aperture stop 25, `is mounted onthecarrier 57 so that when the lenses 22,"23 are in their extremepositions the diaphragm vis very close to theoptical surfacev r11 of thelens `23. The diaphragm housing 112 is rigidly mounted on the carrier57l by membersv113 so that when the lens 23 is moved by the cam 68 thelens 23 moves away from the .diaphragm 111 through a short distance. Theradially extending operating lever 114 of the diaphragm is connected bya short telescopic extension to a ball 115 which is trapped betweenopposed grooves formed in the side walls of a longitudinallyextendingstraight slot 116 in an arm 117. The arm 117 is pivoted at 118about a horizontal axis to a bracket 119 at the frontr endof thebase-plate 55 and extends .upwardlyfand rearwardly from -the pivot 118,

,along the` side of the lens system, and its upper end is .provided witha.guide channel 121 which embraces, and

slides along, .-a quadrant guide plate 122 secured rto the end plate 54.As the carrier moves along the base-plate the operating lever 114of theiris diaphragm is moved .bythe cam action ofthe slot 116 in the arm onthe ball;115fwhich' cooperates `with it. The iris diaphragm is therebyadjusted to maintain the optical system at' a `substantially :constantrelative aperture while the lenses 22 and 23 are moved. The Yarm 117hasta second slot 123which receives a pin 124 on lan arm 125 rigidlymounted ona shaft 126 pivoted in brackets 127, 128. 'The shaft 126 isprovided with a central knob 131 whereby it'may be rotated to cause thepin124 to rotate arm'117 about itspivot 118, thereby to change theinclination of 'the arm 117 relative to the optical axis andconsequently to change the value at which the relative aperture of thesystem is maintained substantially constant while the lenses .22.and23are moved to vary the magnification. The.knob' is .provided with aspring ball detent 1327engaging 4with' any one of a series ofdepressions in a plate .133, vwhichdepressions :aren-marked with thevaluesof 9 relative aperture corresponding to engagement with therespective depressions.

In this example the spherical aberration is substantially zero over thecomplete range of magnification, and coma and chromatic aberration aresimilarly corrected. The astigmatism and field curvature are both verysmall and remain constant over the complete range of magnificationtogether they amount to only approximately -14 wavelengths at theabove-mentioned full aperture and for an angle of field of 6 in theimage space (the negative sign indicating a hollow field).

In this example the system is an afocal telescopic system for producingan image effectively at infinity. For use with effectively non-infiniteimage distances one or more auxiliary lenses may be employed inconjunction with it. When an auxiliary objective lens of focal length9.7 inches is placed after the system of this example the resultantcombination has the same focal length aperture and range ofmagnification as the system described specifically in pendingapplication Serial No. 236,482, now Patent No. 2,663,223.

The invention is not restricted to the details of the foregoing example.For instance, the mechanical details and` the general arrangements ofthe system may be substantially as described in one or more of the otherspecifications mentioned herein, subject to modifications to meet theoptical conditions set out herein. The system is not necessarily anafocal system, it may be designed, for example, as a complete cameraobjective lens.

I claim:

l. A variable magnitication optical system, for producing an image ofcontinuously variable size of an object at a fixed distance from thesystem, comprising two normally stationary lenses, having powers of likesign, and two axially movable lenses, having powers of like sign whichis opposite to the sign of the powers of the normally stationary lenses,all of which lenses are arranged on a common optical axis with themovable lenses between and spaced from the two normally stationarylenses, and in combination with the lens magnification varying means forcontinuously and simultaneously differentially moving the movable lensesin the axial direction of the system according to a law such that thedistance from the normally stationary lenses at which the image of anobject at a fixed distance from the normally stationary lenses isaccurately focussed remains constant, while the size of the said imageis continuously varied during the operation of the magnification varyingmeans, in which system the movable lenses and their range of movementare such that, for one final image position of the system, at a meanposition of their movement they have a joint magnification of minus one,the movable lenses being movable as aforesaid from their mean positionto at least one far position, and in which system the lenses are suchthat the respective differences between the values of sphericalaberration, coma, astigmatism and distortion produced by the movablelenses when they are at their mean position and the corresponding valuesof those four aberrations produced by the movable lenses when they arein their said far position, are substantially equal and opposite to therespective differences between the values of spherical aberration, coma,astigmatism and distortion produced by the said two normally stationarylenses when the movable lenses are at their mean position and thecorresponding values of those four aberrations produced by the said twonormally stationary lenses when the movable lenses are at the said farposition, whereby each of the said four aberrations has substantiallythe same magnitude and sign when the movable lenses are in their saidfar position as when they are in their mean position.

2. A variable magnification optical system according to clairn 1,wherein the lenses are such that the coma and distortion produced by themovable lenses are zero when the movable lenses are at their meanposition and the coma and distortion produced by the said two normallystationary lenses are zero when the movable lenses are in their meanposition, whereby thecoma and distortion of the system are zero when themovable lenses are in their mean position and also when the movablelenses are at their said far position.

3. A variable magnification optical system for producing an image ofcontinuously variable size of an object at a fixed distance from thesystem, comprising two normally stationary lenses, having powers of likesign, and two axially movable lenses, having powers of like sign whichis opposite to the sign of the powers of the normally stationary lenses,all of which lenses are arranged on a common optical axis with themovable lenses between and spaced from the two normally stationarylenses, and in combination with the lens magnification varying means forcontinuously and simultaneously differentially moving the movable lensesin the axial direction of the system according to a law such that thedistance from the normally stationary lenses at which the image of anobject at a fixed distance from the normally stationary lenses isaccurately focussed remains constant. while the size of the said imageis continuously varied during the operation of the magnification varyingmeans, in which system the movable lenses and their range of movementare such that, for one final image position of the system, at a meanposition of their movement they have a joint magnification of minus one,the movable lenses being movable as aforesaid from their mean positionto at least one far position and in which system the said lenses aresuch that their joint spherical aberration is zero, and the lenses aresuch that the respective differences between the values of sphericalaberration, corna and astigmatism produced by the movable lenses whenthey are at their mean position and the corresponding values of thosethree aberrations produced by the movable lenses when they are at theirsaid far position are substantially equal and opposite to the respectivedifferences between the values of spherical aberration coma andastigmatism produced by the said two normally stationary lenses when themovable lenses are at their mean position and the corresponding valuesof those three aberrations produced by the said two normally stationarylenses when the movable lenses are at the said far position.

4. A variable magnification optical system according to claim 3 whereinthe lenses are such that the system has zero spherical aberration andzero coma over the range of movement of the movable lenses between theirmean position and their said far position, whereby the astigmatism ofthe system is constant for movement of the movable lenses between theirmean position and their said far position.

5. A variable magnification optical system, 'for pro-- ducing an imageof continuously variable size of an ob ject at a fixed distance from thesystem, comprising two normally stationary lenses, having powers of likesign,l and two axially movable lenses, having powers of likey sign whichis opposite to the sign of the powers of the normally stationary lenses,all of which lenses are ar ranged on a common optical axis with themovable lenses: between and spaced from the normally stationary lenses.and in combination with the lens magnification varying means forcontinuously and simultaneously differentially' moving the movablelenses in the axial direction of thesystem according to a law such thatthe distance from the normally stationary lenses at which the image ofan object at a fixed distance from the normally stationaryv lenses isaccurately focussed remains constant, while thesize of the said image iscontinuously varied during the operation of the magnification varyingmeans, in which` system the movable lenses and their range of movementare such that, for one final image position of the system, at a meanposition of their movement they have a joint magnification of minus one,the movable lenses being movable aforesaidfrom their mean position ,toat least one far position, the said lenses satisfying the equations:

in which equations the operator d denotes the diterence between thevalue of an aberration produced when the said movable lenses are at thesaid far position and the corresponding value of that aberration whenthe said movable lenses are at their mean position, the subscript mdenotes anaberration produced jointly by the said movable lenses, thesubscript ns denotes an aberration produced jointly by the said twonormally stationary lenses, S1 denote spherical aberration, S2 denotescoma, Sa de notes astigmatism and S5 denotes distortion.

6. A variable magnification optical system, for producing an image ofcontinuously variable size of an object at a fixed distance from thesystem, comprising two normally stationary lenses, having powers of likesign, and two axially movable lenses, having powers of like sign whichis opposite to the sign of the powers of the normally stationary lenses,all of which lenses are arranged on a common optical axis with themovable lenses between and spaced from the two normally stationarylenses, and in combination with the lens magnification varying means forcontinuously and simultaneously differentially moving the movable lensesin the axial direction of the system according to a law such that thedistance from the normally stationary lenses at which the image of anobject at a fixed distance from the normally stationary lenses isaccurately focussed remains constant, while the size of the said imageis continuously varied during the operation of the magnification varyingmeans, in which system the movable lenses and their range of movementare such that, for one final image position of the system, at a meanposition of their movement they have a joint magnification of minus one,the movable lenses being movable as aforesaid from their mean positionto at least one far position, the spherical aberration produced jointly12 by the said lenses being zero, and the said lenses satisfying theequations:

i d(S1)11tlvl(S1)v1s=0 Y d(S2)m+d(S2)nsv=0, Vand y ll(S3)11t-jd(53)ns=0'in which'equations the operator d denotes the diierence between thevalue of an aberration produced when the said movable lenses are at thesaid far position and the corresponding value of that aberration whenthe said movable lenses are at their mean position, the subscript mdenotes an aberration produced jointly by the said movable lenses,A thesubscript ns denotes an aberration produced jointly by the said twonormally stationary lenses, S1 denotes spherical aberration, S2 denotescoma, and S3 denotes astigmatism.

7. A variable magnification optical system according to claim l, whereinthe movable lenses are compound and optically identical at least inrespect of the radii of their optical surfaces, their glasses and thethickness of their components, and are arranged with their refractingsurfaces symmetrically positioned about a point on the axis mid-waybetween the said two movable lenses, and Wherein the said four lensesare such that their joint spherical aberration is zero and that theirjoint astigmatism is such, in relation to their total lield curvature,that the tangential image surface lies in the paraxial focal plane,whereby the system vis completely corrected for primary aberrations inrespect of object and image positions eiectively symmetricallypositioned with respect to the system.

References Cited in the tile of this patent UNITED STATES PATENTS2,165,341 Capstaff et al July 11, 1939 2,235,364 Gramatzki Mar. 18, 19412,353,565 Kaprelian JulyV 1l, 1944 2,514,239 Hopkins July 4, 19502,566,485 Cuvillier Sept. -4, 1951 2,578,574 Miles Dec. 11, 19512,649,025 Cook Aug. 18, 1953 2,663,223 Hopkins Dec. 22, 1953

